Asadullah Amarkhil said fighting in Kunduz city had stopped, and there were large numbers of Taliban casualties.
On Monday, Taliban fighters appeared to have breached the strategic northern city.
The fighting came a day before a major conference in Brussels to raise funds to ensure Afghan stability.
Kunduz was briefly captured by the Taliban in September 2015 in what was a major victory.
After days of back-and-forth fighting, government forces, backed by Nato, recaptured the city.
Taliban militants entered Kunduz early on Monday and seized some central areas.
Its spokesman, Zabihullah Mujahid, said on Twitter that it was a "massive operation". The Taliban later said they had seized the roundabout and several checkpoints, but did not claim to have captured the city.
But by late on Monday, Nato forces and local police said they were back in control, with additional troops, including special forces, being flown in.
The governor said in the early hours of Tuesday that the clear-up operation was continuing but people should "start their daily life and go to their work".
"If there is any Taliban hiding inside the houses, we will clear that after dawn."
At least one member of the security forces was killed, while there were various conflicting reports on the number of militant casualties.
Kunduz police chief Mohammad Qasim Jangalbagh told AFP that "hundreds of Taliban fighters" were killed.
The capture of Kunduz by the Taliban last September was a huge blow to the country's Western-backed government. The militants abandoned the city after four days but they had proved their growing capability by taking their first major city,
The group raided Tarin Kot, the provincial capital of Uruzgan, last month.
Afghan government forces are estimated to have control over no more than two-thirds of Afghanistan.
The two-day conference in Brussels, attended by Afghan President Ashraf Ghani and led by the EU, aims to raise billions of dollars to fund Afghanistan until 2020.
Officials have said financial support from the international community is essential to secure the country's stability.
The EU's Special Representative for Afghanistan Franz-Michael Mellbin said the conference was "buying four more years for Afghanistan" as well as seeking a "realistic" peace process.
"If we don't achieve peace, it's simply going to be extremely costly for the foreseeable future," he told Reuters.